Transition Matrix for Nucleon-Nucleon Scattering. II

Abstract

The Fredholm reduction of the singular integral equation satisfied by the reactance matrix, which was developed in a previous paper, is extended so as to constitute a complete and unified Fredholm formalism for the various integral equations which occur in the momentum‐space formulation of two‐body (potential) scattering problems. The essential simplification which permits this unified treatment is the demonstration of the formal similarity of the scattering integral equations, whether or not part of the interaction includes a hard core. The principal result consists in an apparatus which is useful in performing those two‐body calculations which occur in investigations of high‐energy nucleon‐nucleus scattering; in particular, the technique is used to obtain the solutions of integral equations satisfied by transition matrices which appear typically in multiple‐scattering theories. The relation between the uniqueness of solutions of the scattering integral equations and the validity of the Fredholm formalism is also discussed. Finally, some methods which were previously considered for obtaining approximate solutions of the Fredholm equations are generalized.